Finite difference scheme for a high order nonlinear Schrödinger equation with localized damping
DOI:
https://doi.org/10.24193/subbmath.2019.2.03Keywords:
HNLS, Soliton Theory, Localized damping, Finite Difference Methods.Abstract
In this work we present a finite difference scheme used to solvea High order Nonlinear Schrödinger Equation with localized damping.
These equations can model the propagation of solitons travelling in fiber
optics ([3], [10]). The scheme is designed to preserve the numerical en-
ergy at L 2 level, and control the energy at H 1 level for a suitable choose
on the equation’s parameters, and when there is no damping in effect.
Numerical results will be shown.
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